This is sort of on the line of making purchases.
We just got back from the Eastern Caribbean a few weeks ago.
One thing I would recommend, although it can be very "crowded", is the straw markets on these islands. They all seem to have the same thing, or something similiar, but you can really save money buy purchasing from them. You can get 4 T-shirts for $10.00, which are pretty nice. My friend also bought a very nice bag to carry her beach, etc. things in for $10.00. These were very good deals. I noticed there were small buildings a few blocks away with almost the same thing, only higher priced. The difference, they have "overhead" to pay for, so thus they have to charge more.
In St. Thomas, if you want jewelry without paying tax, that is the place to go. Compare the prices to the ship, and normally you will come out ahead. The ship does run specials each day, and you can get some beautiful beaded/sequen purses for $15.00, and watches the same price.